Turbomachinery devices, such as gas turbine engines and steam turbines, operate by exchanging energy with a working fluid using alternating rows of rotating blades and non-rotating vanes. Each blade and vane has an airfoil portion that interacts with the working fluid.
Airfoils have natural vibration modes of increasing frequency and complexity of the mode shape. The simplest and lowest frequency modes are typically referred to as first bending, second bending, and first torsion. First bending is a motion normal to the flat surface of an airfoil in which the entire span of the airfoil moves in the same direction. Second bending is similar to first bending, but with a change in the sense of the motion somewhere along the span of the airfoil, so that the upper and lower portions of the airfoil move in opposite directions. First torsion is a twisting motion around an elastic axis, which is parallel to the span of the airfoil, in which the entire span of the airfoil, on each side of the elastic axis, moves in the same direction.
It is known that turbomachinery blades are subject to destructive vibrations due to unsteady interaction of the blades with the working fluid. One type of vibration is known as flutter, which is an aero-elastic instability resulting from the interaction of the flow over the blades and the blades' natural vibration tendencies. When flutter occurs, the unsteady aerodynamic forces on the blade, due to its vibration, add energy to the vibration, causing the vibration amplitude to increase. The vibration amplitude can become large enough to cause structural failure of the blade. The operable range, in terms of pressure rise and flow rate, of turbomachinery is restricted by various flutter phenomena.
Lower frequency vibration modes, i.e., the first bending mode and first torsion mode, are the vibration modes that are typically susceptible to flutter. In one approach to avoid or reduce flutter, it has been a conventional practice to increase the first bending and first torsion vibration frequencies of the blades, including utilizing mix-tuning principles that promote blade-to-blade differences in blade natural frequency and mode shape.
In highly loaded last row blades of typical power generation steam turbines, one strong contributor to aero-elastic instability is attributed to the shock associated with the supersonic expansion downstream of the blade passage throat, which may be referred to as shock induced flutter. Shock induced flutter may exist under either stalled or unstalled flow conditions, as is referenced to the presence or absence, respectively, of a gross separation of the flow about the airfoil surface as a result of inlet incidence angle effects. Under such conditions, the strength of the destabilizing forces associated with the shock flow field may be increased by the regularity of the blade-to-blade flow field behaviour.